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Cross shaft

Cross_shaft
Cross shaft

Values for calculation

$T$ $\mathrm{Nm}$
$r$ $\mathrm{mm}$
$s$ $\mathrm{mm}$
$L$ $\mathrm{mm}$
$G$ $\mathrm{MPa}$

Calculation

Coefficient $ C $

$$C=1.1266-0.321\cdot\cfrac{r}{s}+3.1519\cdot\left(\cfrac{r}{s}\right)^2-14.347\cdot\left(\cfrac{r}{s}\right)^3+15.223\cdot\left(\cfrac{r}{s}\right)^4-4.7767\cdot\left(\cfrac{r}{s}\right)^5$$

Coefficient $ B_M $

$$B_M=0.601+0.1059\cdot\cfrac{r}{s}-0.918\cdot\left(\cfrac{r}{s}\right)^2+3.7335\cdot\left(\cfrac{r}{s}\right)^3-2.8686\cdot\left(\cfrac{r}{s}\right)^4$$

Coefficient $ B_N $

$$B_N=-0.3281+9.1405\cdot\cfrac{r}{s}-42.52\cdot\left(\cfrac{r}{s}\right)^2+109.04\cdot\left(\cfrac{r}{s}\right)^3-133.95\cdot\left(\cfrac{r}{s}\right)^4+66.054\cdot\left(\cfrac{r}{s}\right)^5$$

Polar moment of inertia

$$K=2\cdot C\cdot s^4$$

Angle of twist

$$θ=\cfrac{T\cdot 10^3\cdot L}{K\cdot G}$$

Torsion stress at $ M $

$$τ_{max-at-M}=\cfrac{10^3\cdot T\cdot B_M}{s^3}$$

Torsion stress at $ N $

$$τ_{max-at-N}=\cfrac{10^3\cdot T\cdot B_N}{s^3}$$

Requirements

$$0.3 \le\cfrac{r}{s} \le 0.5$$